USING OF MULTILAYER NEURAL NETWORKS FOR THE SOLVING SYSTEMS OF DIFFERENTIAL EQUATIONS

The article considers the study of methods for numerical solution of systems of differential equations using neural networks. To achieve this goal, thefollowing interdependent tasks were solved: an overview of industries that need to solve systems of differential equations, as well as implemented amethod of solving systems of differential equations using neural networks. It is shown that different types of systems of differential equations can besolved by a single method, which requires only the problem of loss function for optimization, which is directly created from differential equations anddoes not require solving equations for the highest derivative. The solution of differential equations’ system using a multilayer neural networks is thefunctions given in analytical form, which can be differentiated or integrated analytically. In the course of this work, an improved form of constructionof a test solution of systems of differential equations was found, which satisfies the initial conditions for construction, but has less impact on thesolution error at a distance from the initial conditions compared to the form of such solution. The way has also been found to modify the calculation ofthe loss function for cases when the solution process stops at the local minimum, which will be caused by the high dependence of the subsequentvalues of the functions on the accuracy of finding the previous values. Among the results, it can be noted that the solution of differential equations’system using artificial neural networks may be more accurate than classical numerical methods for solving differential equations, but usually takesmuch longer to achieve similar results on small problems. The main advantage of using neural networks to solve differential equations` system is thatthe solution is in analytical form and can be found not only for individual values of parameters of equations, but also for all values of parameters in alimited range of values.

Mechanical movement data acquisition method based on the multilayer neural networks and machine vision in a digital twin environment

Background: Digital twin requires virtual reality mapping and optimization iteration between physical devices and virtual models. The mechanical movement data collection of physical equipment is essential for the implementation of accurate virtual and physical synchronization in a digital twin environment. However, the traditional approach relying on PLC (programmable logic control) fails to collect various mechanical motion state data. Additionally, few investigations have used machine visions for the virtual and physical synchronization of equipment. Thus, this paper presents a mechanical movement data acquisition method based on multilayer neural networks and machine vision. Methods: Firstly, various visual marks with different colors and shapes are designed for marking physical devices. Secondly, a recognition method based on the Hough transform and histogram feature is proposed to realize the recognition of shape and color features respectively. Then, the multilayer neural network model is introduced in the visual mark location. The neural network is trained by the dropout algorithm to realize the tracking and location of the visual mark. To test the proposed method, 1000 samples were selected. Results: The experiment results shows that when the size of the visual mark is larger than 6mm, the recognition success rate of the recognition algorithm can reach more than 95%. In the actual operation environment with multiple cameras, the identification points can be located more accurately. Moreover, the camera calibration process of binocular and multi-eye vision can be simplified by the multilayer neural networks. Conclusions: This study proposes an effective method in the collection of mechanical motion data of physical equipment in a digital twin environment. Further studies are needed to perceive posture and shape data of physical entities under the multi-camera redundant shooting.

Heart Disease Diagnosis by Neural Networks

In the present time the Mortality rate will be increased all around the world on their daily basis. So the cause for this might possibly be largely ascribe to the developing in the numbers of the patients with the cardiovascular patient’s diseases. To aggravate the cases, many physicians that have been known for the misdiagnosis of the patients announce heart related ailments. In this research paper, the intelligent systems have been designed in which they will help in the successful diagnosis of the forbearing to avoiding misdiagnosis. In the dataset of a UCI stat log of heart disease that will be using in this investigation. The dataset contains 14 attributes which are essential in the diagnosis of the heart diseases. A system is sculpted on the multilayer neural networks trained with convolutional & simulated convolutional neural networks. The identification of 89% was acquired from the testing of the networks.

A comparison of activation functions in multilayer neural network for predicting the production and consumption of electricity power

Predicting electricity power is an important task, which helps power utilities in improving their systems’ performance in terms of effectiveness, productivity, management and control. Several researches had introduced this task using three main models: engineering, statistical and artificial intelligence. Based on the experiments, which used artificial intelligence models, multilayer neural networks model has proven its success in predicting many evaluation datasets. However, the performance of this model depends mainly on the type of activation function. Therefore, this paper introduces an experimental study for investigating the performance of the multilayer neural networks model with respect to different activation functions and different depths of hidden layers. The experiments in this paper cover the comparison among eleven activation functions using four benchmark electricity datasets. The activation functions under examination are sigmoid, hyperbolic tangent, SoftSign, SoftPlus, ReLU, Leak ReLU, Gaussian, ELU, SELU, Swish and Adjust-Swish. Experimental results show that ReLU and Leak ReLU activation functions outperform their counterparts in all datasets.